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/dev/random is said to by cryptographically secure, and unpredictable, as it gathers data from external sources, influenced by human timing interactions with computers, to fill the entropy pool. As such, this is a quick way to do a true random fair-6 dice roll. Using this method, you could easily create passphrases with Diceware http://diceware.com.

for i in {1..5}; do echo -n $((0x$(head -c5 /dev/random|xxd -ps)%6+1)); done; echo

You are absolutely right. However, it's biased away from 5 and 6 by 2 percent. So, you could update the command to read more bytes. Reading 2 bytes would produce a bias away from 5 and 6 by 9 thousandths of one percent. Reading 3 bytes would produce a bias away from 5 and 6 of 4 one-hundred thousandths by one percent. I would be willing to bet that standard fabricated dice have a larger bias towards some numbers than that. So, for practical purposes, reading only 10 bytes, would be more than sufficient, and certainly "close enough". I've updated the post.